Abstract
We study the dependence of magnetic properties: Curie temperature, mean and local magnetic moments—on the type of crystal lattice and average number of d electrons per atom. The problem is considered in two approximations: with spin fluctuations not taken into account, in the Stoner mean field theory, and with spin fluctuations taken into account, in the dynamic spin fluctuation theory (DSFT). In the DSFT, we obtain an analogue of the Slater–Pauling curve for the mean magnetic moment at finite temperatures. Numerical results in the DSFT are in qualitative agreement with experiment: with magnetic phase diagram and dependence of magnetic moment on concentration in ferromagnetic alloys.
REFERENCES
U. Köbler, “Sample-size dependent temperature dependence of the spontaneous magnetization,” J. Magn. Magn. Mater. 491, 165632 (2019). https://doi.org/10.1016/j.jmmm.2019.165632
B. Leedahl, A. V. Korolev, I. S. Zhidkov, S. L. Skornyakov, V. I. Anisimov, A. S. Belozerov, A. I. Kukharenko, E. Z. Kurmaev, V. I. Grokhovskii, S. O. Cholakh, and A. Moewes, “Searching for pure iron in nature: The Chelyabinsk meteorite,” RSC Adv. 6, 85844–85851 (2016). https://doi.org/10.1039/c6ra16598b
N. V. Mushnikov, A. G. Popov, V. S. Gaviko, A. V. Protasov, N. M. Kleinerman, O. A. Golovnya, and S. P. Naumov, “Peculiarities of phase diagram of Fe–Ni system at Ni concentrations 0–20 at %,” Acta Mater. 240, 118330 (2022). https://doi.org/10.1016/j.actamat.2022.118330
A. I. Lichtenstein, M. I. Katsnelson, and G. Kotliar, “Finite-temperature magnetism of transition metals: An ab initio dynamical mean-field theory,” Phys. Rev. Lett. 87, 067205 (2001). https://doi.org/10.1103/physrevlett.87.067205
Y. Kakehashi, Modern Theory of Magnetism in Metals and Alloys, Springer Series in Solid-State Sciences, Vol. 175 (Springer, Berlin, 2013). https://doi.org/10.1007/978-3-642-33401-6
A. S. Belozerov, I. Leonov, and V. I. Anisimov, “Magnetism of iron and nickel from rotationally invariant Hirsch–Fye quantum Monte Carlo calculations,” Phys. Rev. B 87 (12), 125138 (2013). https://doi.org/10.1103/physrevb.87.125138
A. V. Ruban, S. Khmelevskyi, P. Mohn, and B. Johansson, “Temperature-induced longitudinal spin fluctuations in Fe and Ni,” Phys. Rev. B 75, 054402 (2007). https://doi.org/10.1103/physrevb.75.054402
D. Gambino, M. A. Brännvall, A. Ehn, Y. Hedström, and B. Alling, “Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach,” Phys. Rev. B 102, 014402 (2020). https://doi.org/10.1103/physrevb.102.014402
N. B. Melnikov and B. I. Reser, “Magnetism of metals in the dynamic spin-fluctuation theory,” Phys. Met. Metallogr. 117, 1328–1383 (2016). https://doi.org/10.1134/s0031918x16130020
N. B. Melnikov and B. I. Reser, Dynamic Spin-Fluctuation Theory of Metallic Magnetism (Springer, Berlin, 2018). https://doi.org/10.1007/978-3-319-92974-3
G. V. Paradezhenko, D. Yudin, and A. A. Pervishko, “Random iron-nickel alloys: From first principles to dynamic spin fluctuation theory,” Phys. Rev. B 104, 245102 (2021). https://doi.org/10.1103/physrevb.104.245102
L. J. Swartzendruber, V. P. Itkin, and C. B. Alcock, “The Fe–Ni (iron–nickel) system,” J. Phase Equilib. 12, 288–312 (1991). https://doi.org/10.1007/bf02649918
W. Xiong, H. Zhang, L. Vitos, and M. Selleby, “Magnetic phase diagram of the Fe–Ni system,” Acta Mater. 59, 521–530 (2011). https://doi.org/10.1016/j.actamat.2010.09.055
H. Ebert, S. Mankovsky, and S. Wimmer, “Electronic structure: Metals and insulators,” in Handbook of Magnetism and Magnetic Materials, Ed. by M. Coey and S. Parkin (Springer, Berlin, 2020), pp. 1–73. https://doi.org/10.1007/978-3-030-63101-7_4-1
A. Ayuela and N. H. March, “The magnetic moments and their long-range ordering for Fe atoms in a wide variety of metallic environments,” Int. J. Quantum Chem. 110, 2725–2733 (2010). https://doi.org/10.1002/qua.22764
V. I. Grebennikov, “Dynamical theory of thermal spin fluctuations in metallic ferromagnets,” Phys. Solid State 40, 79–86 (1998). https://doi.org/10.1134/1.1130238
B. I. Reser and V. I. Grebennikov, “Effect of dynamic nonlocal spin fluctuations on the temperature dependence of magnetic properties of ferromagnetic metals,” Phys. Met. Metallogr. 85, 20–27 (1998).
G. V. Paradezhenko, N. B. Melnikov, and B. I. Reser, “Numerical continuation method for nonlinear system of scalar and functional equations,” Comput. Math. Math. Phys. 60, 404–410 (2020). https://doi.org/10.1134/s0965542520030112
B. I. Reser, G. V. Paradezhenko, and N. B. Melnikov, “Program suite MAGPROP 2.0,” (Russian Federal Service for Intellectual Property (ROSPATENT), 2018).
V. L. Moruzzi, J. F. Janak, and A. R. Williams, “Calculated Electronic Properties of Metals,” (Pergamon, New York, 1978). https://doi.org/10.1016/C2013-0-03017-4
J. C. Slater, Quantum Theory of Molecules and Solids Vol. 4: The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974).
R. M. Bozorth, Ferromagnetism (Wiley-IEEE, New York, 1993). https://doi.org/10.1109/9780470544624
Y. Kakehashi, “Magnetism in amorphous transition metals,” Phys. Rev. B 43, 10820–10831 (1991). https://doi.org/10.1103/physrevb.43.10820
H. Ehrenreich and L. M. Schwartz, “The electronic structure of alloys,” in Solid State Physics, Ed. by H. Ehrenreich, F. Seitz, and F. S. D. Turnbull (Academic, New York, 1976), Vol. 31, pp. 149–286. https://doi.org/10.1016/s0081-1947(08)60543-3
J. Nelson and S. Sanvito, “Predicting the Curie temperature of ferromagnets using machine learning,” Phys. Rev. Mater. 3, 104405 (2019). https://doi.org/10.1103/physrevmaterials.3.104405
Z. Rao, D. Ponge, F. Körmann, Y. Ikeda, O. Schneeweiss, M. Friák, J. Neugebauer, D. Raabe, and Z. Li, “Invar effects in FeNiCo medium entropy alloys: From an Invar treasure map to alloy design,” Intermetallics 111, 106520 (2019). https://doi.org/10.1016/j.intermet.2019.106520
ACKNOWLEDGMENTS
We are grateful to the reviewers for the useful comments.
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The work was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (theme “Quantum” no. 122021000038-7).
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Melnikov, N.B., Gulenko, A.S. & Reser, B.I. Relation between Magnetism and Electronic Structure of 3d-Metal Alloys in the Stoner Theory and in the DSFT. Phys. Metals Metallogr. 125, 49–55 (2024). https://doi.org/10.1134/S0031918X23602275
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DOI: https://doi.org/10.1134/S0031918X23602275